A person's beracha rishona and beracha acharona are not always connected, in terms of one ending with the other. You can have situations, according to some Rishonim (Tosefos and Rosh in Arvei Pesachim, cited by Rama O.C. 178:2) where a person needs to make a new beracha rishona even though he has not made a beracha acharona, as in the case of leaving and coming back in the middle of eating. What ends a beracha rishona is hesech hada'as, the removal of your "awareness" from the eating on which you made the beracha. Mishna Berura 179:3 says that even a firm mental decision to stop eating constitutes such a hesech hada'as.
A beracha acharona constitutes a hesech hada'as, because it is a declaration that you are done eating. Mishna Berura states this explicitly in 190:1 regarding benching. Therefore, you would need to make a new blessing, but not because your beracha acharona "ended" your beracha rishona, but because your beracha acharona amounted to, or was a manifestation of, a hesech hada'as.